"This is the most special day in my life", Coric, the world number 18, told reporters as local media hailed him as a "hero".
The victor on the outdoor clay court along the Dalmatian Coast will meet defending champion France in the November 23-25 final.
Both Cilic and Coric had won their singles matches on Friday, before the USA cut Croatia's lead to 2-1 as Mike Bryan and Ryan Harrison beat Ivan Dodig and Mate Pavic in a dramatic doubles rubber on Saturday.
"They're good at tennis", Courier said.
Doubles specialist Mike Bryan's decision to come out of Davis Cup retirement gave the United States a much-needed lift.
Yet for a moment, after Coric had capitulated 7-0 in the first set breaker and 13-11 in the third set decider, the shocked fans in the Dalmatian resort feared Croatia could be on the wrong end of one of the competition's unlikeliest comebacks.
"I had a couple of dips - in the second and the fourth. I really wasn't paying attention", Tiafoe said. "I'm young and I'm going to learn from that".
"I just hung in there". "After being 6-1 down in the tiebreak, I just played aggressively and from then on the pressure just builds".
Ramos belatedly received public backing from the International Tennis Federation (ITF) and took his place in the chair for Cilic's routine 6-1 6-3 7-6 (7-5) win over Tiafoe.
Carlos Ramos, the chair umpire who penalized Serena Williams in the U.S. Open final, officiated the second match without incident. The American great argued she wasn't being treated the same as some male players.
"I normally go somehow around my back", he said. "I was more anxious about the person across the net than the official". "My level today was not at the top". "That's for sure", Querrey said. Mike and Ryan gained a huge boost after that and they broke their rivals in games 10 and 12 to steal the opener 7-5.
Croatia extended its ideal record over the U.S.to 5-0.
Croatia secured their place in the Davis Cup final with a 3-2 victory over the US in Zadar. France advanced with a 3-2 win.
In Lille there was relief that the Croatians had won as it guaranteed the final would be a home tie for France.
Croatia is looking to extend its flawless record over the U.S.to 5-0.
French number one Lucas Pouille battled for three hours 41 minutes, coming from a set down, to somehow get past Spain's Roberto Bautista Agut 3-6 7-6 (5) 6-4 2-6 6-4 to put his country 2-0 ahead.
The meaningless last singles rubber, between Dennis Novak and Jordan Thompson, was canceled.
On hardcourt in France Benoit Paire defeated Spain's Pablo Carreno-Busta 7-5, 6-1, 6-0 in the first singles on Friday.
In World Group Playoffs action past powerhouses Australia and Switzerland were upset, leaving their status in limbo as the ITF prepares to announce which teams will participate in next year's restructured Davis Cup.